大腦進行運作的機制一向是科學與醫學的研究重點，本論文使用快速傅立葉轉換(FFT)和多尺度熵(MSE)的方法，分析大腦進行數學認知行為的空間能量分佈特徵，兩類分析方法的實驗結果同時指出，大腦前額葉與頂葉為數學認知行為的主要激發區域，大腦枕葉的能量特徵相對較不顯著，而四類基礎數學運算以加法及乘法運算對大腦負荷度較低，減法及除法對大腦負荷度則相對較高。本研究另外探討當我們數學計算時，常伴隨出現的空間旋轉概念(如：建築工程、向量計算…等)的空間能量特徵，發現其大腦特徵與數學運算時高度相似，都是以大腦前額葉為顯著特徵區域，而我們也使用適用於非穩態訊號的經驗模態分解法(EMD)進行濾波，及線性鑑別分析法(LDA)與最近鄰居法(NNR)辨識想像順時針旋轉與逆時針旋轉的腦電波，實驗結果以FZ電極與FCZ電極的組合辨識率最高，四位受測者平均辨識率可達80.7%，辨識率較想像四肢活動雖無顯著提升，但證實了想像幾何旋轉動作為有效的想像辨識標的。

The mechanism of how the brain functions and processes the data has always been the major research concern in both scientific and medical fields. This thesis presents the spatial energy distribution characteristics when the brain doing mathematical cognitive behaviors via the application of FFT and MSE. And the results of both analyses had pointed out that frontal lobe and parietal lobe of the brain are the major stimulating areas for mathematical cognitive behaviors, while the occipital lobe holds comparatively less obvious energy characteristics. Meanwhile, among the four basic operations of arithmetic,
subtraction and division put more loadings to our brain, compared to addition and multiplication. This research also probes into the spatial energy distribution characteristics for 3D rotating concepts that we applied while doing math
calculations, such as building construction programs and vector quantity calculations. We have discovered a highly similarity as doing arithmetic. There are both more energetic performances on the frontal lobe of the brain. We also use LDA and NNR, to recognize the EEGs while imagining clockwise rotations and anticlockwise ones. The outcomes show that the combination of FZ electrode and FCZ electrode has the best recognition rate, an average of 80.7% among our
experimental subjects. Though the rate doesn’t suggest a higher recognizablity than picturing the limb activities, it proves that imagining geometric rotation surely is a valid alternative for imagining recognition.

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